Dynamic alloy correction gauge

ABSTRACT

A method of calculating the thickness of a sheet material comprising directing a beam of photons against the sheet material from a photon source (1) located on one side of said sheet material (7), detecting reflected radiation from said sheet material in a first detector (2) located on the same side of said sheet material and detecting transmitted radiation in a second detector (5) located on the opposite side of the said sheet material, combining the signals of transmitted and reflected photon beams, measuring and processing the data from both detectors for a number of calibrating samples, obtaining the thickness as a function of the detected data and applying this function to determine the unknown thickness of a sample. Apparatus for carrying out the method of the invention is also disclosed.

For several decades measurement of sheets of metal in production plantswhere the sheets are continuously moving, such as steel mills, beveragecan or automobile factories, has been accomplished by measuring theabsorption of a beam of radiation. This method of measurement isdescribed in particular in the paper "Steel Measurement by RadiationGauges" by D. Gignoux, published in "Steel Technology International"(1990) on pages 257 to 260.

When the radiation beam consists of electrons, i.e. beta radiation, themeasurement of the absorption by the material can be translated readilyinto a measure of mass per unit area of the material. For someapplications the mass per unit area is the quantity that is used torepresent thickness. In other cases, it suffices to divide the mass perunit area by the density to obtain the physical thickness expressed inunits of length. Beta radiation cannot be obtained in very intense beamsas a practical matter, so that the measurements are too slow to besuitable for modern mill control computers. Another problem is that betaradiation is suitable to measure relatively thin material only.

X-ray beams are used the most often. They can be obtained with enoughintensity and their energy can be varied so that it is possible tomeasure aluminium, steel, other metals and some plastics materials.However, the figure obtained for the absorption by a sheet of a certainmetal is very much dependent on the composition of the metal.

For instance, when gauging aluminium, if the sheet contains a smallpercentage of some metal higher than aluminium in the periodic table ofelements such as zinc, iron or copper, measurement may be inaccurate ifthe composition is not taken into account. If the composition is known,it is quite possible to relate the thickness to the absorptionmeasurement. In most cases, the relation consists essentially of usingthe basic function relating absorption to thickness of pure metal andmultiplying the result by an alloy factor. The requirement of modernmills for an accuracy of measurement of 0.1% requires, for certainaluminium alloys, that the composition be known very accurately, this isnot really possible. Furthermore, sometimes the variation in compositionbetween one end of the coil and the other is sufficiently large tocreate errors. Several schemes have been proposed for solving thisproblem. One consists of coupling the X-ray gauge to a gauge using abeam of beta particles generally produced by a radioisotope. This hasseveral disadvantages in practice as it requires 2 different gaugesmeasuring at 2 different points. Another scheme is the possibility ofusing 2 X-ray gauges producing beams of two different energies so thatthey do not have the same absorption characteristic. This method is goodonly when the concentration of only one alloying element varies. Forinstance, zinc in aluminium is uncertain, also the two measurements needto be made with an extreme degree of accuracy for the ultimate result tobe itself of sufficient accuracy.

According to the invention, there is provided a method of calculatingthe thickness of a sheet material comprising directing a beam of photonsagainst the sheet material from a photon source located on one side ofsaid sheet material, detecting reflected or "backscattered" radiationfrom said sheet material in a first detector located on the same side ofsaid sheet material and detecting transmitted radiation in a seconddetector located on the opposite side of the said sheet material,combining the signals of transmitted and reflected or "backscattered"photon beams, measuring and processing the data from both detectors fora number of calibrating samples, obtaining the thickness as a functionof the detected data and applying this function to determine the unknownthickness of a sample.

The invention also provides an apparatus for calculating the thicknessof a sheet material comprising a source of photons located on one sideof said sheet material, adapted to direct a beam of photons from saidphoton source against said sheet material, a first detector located onthe same side of said sheet material for detecting reflected or"backscattered" radiation from said sheet material and a second detectorlocated on the opposite side of the said sheet for detecting transmittedradiation, computing means for combining the signals of transmitted andreflected or "backscattered" photon beams and computing and signalprocessing means for measuring and processing the data from bothdetectors for a number of calibrating samples, whereby the thickness ofthe sheet material is obtained as a function of the detected data andthe function is applied to determine the unknown thickness of a sample.

In a preferred embodiment of an apparatus for carrying out theinvention, the first detector is disposed so that it surrounds thephoton beam source.

In another embodiment of the invention, the source of photons is anX-ray generator.

In carrying out the method of the invention, a computer means carryingout the measurement and processing of the signals uses a polynomial intwo variables employing a best-fit method and in yet another aspect ofthe invention, the best-fit method is a least square approximation.

In a further embodiment of the method according to the invention, thecomputing means are employed to fit a linear function through threepoints surrounding an unknown point, said linear function being thenused to calculate the unknown thickness, while in an alternativeembodiment of the invention, the computer functions with a quadraticfunction and six data points. The invention further provides a method ofcalibration which includes the step of using a sample placed in the beamof photons, memorising the data representing beam intensity received bythe detector and multiplying the data obtained in a measurement by theratio of variation of the data obtained by the sample. Alternatively,the calibration includes the step of multiplying the intensities of thebeam of radiation and the reflected or "backscattered" beam by the ratioof these values obtained at the time of measurement to the same valuesobtained at the time of calibration.

The present invention relates to a method, to be described herein, whichconsists of utilizing the information from a transmission beam of X-rayradiation and also that of a reflected or "backscattered" beam. Whenevera beam of photons encounters matter, three phenomena of interest forgauging purposes occur: First, the beam goes through the materialyielding on the other side a transmitted beam. Second, fluorescenceoccurs at frequencies or energy levels that are characteristics of theelements in question and third, a portion of the beam is scattered. Forour purpose it will suffice to consider the reflected beam, hereinafteralso referred to as the backscattered beam, as a diffuse reflection ofthe initial beam by the material, bearing in mind that this reflectionis not a surface phenomenon but occurs throughout the material. For allthe materials considered here, fluorescence occurs at low energy levelsof less than 10 kv. It is therefore easy to differentiate betweenfluorescence and backscattered beams as the latter has an energy mostlyhigher than that of the fluorescence radiation.

The method is suitable for any alloy or mixtures where small compositionvariation cause variations in absorption. Aluminium and stainless steelare of particular interest.

Prior art regarding this matter has been found in U.S. Pat. Nos.3,210,545 dated Oct. 5, 1965 Barnett, 4,047,029 dated Sep. 6, 1977,Allport and 4,803,715 Cho, dated Feb. 7, 1989.

However, the matter presented by these inventors applies only to thecase where the alloy correction factor is known and only the variationbetween the true alloy correction factor and the assumed but inaccuratealloy correction factor is determined by the measurement method.

The present invention seeks to provide a method of measurement in whicha sheet of any alloy, for instance an alloy of aluminium, can bemeasured without the need to know the approximate composition of thematerial. The invention also seeks to provide a measuring device that isfast enough to be used for modern mill control computers. The inventionfurther seeks to provide a measurement which has little of the smallfluctuations of the measurement with time, commonly referred to as"noise" by signal processing engineers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a preferred embodiment of the invention.

FIG. 2 is an example of curve fitting for the thicknesses X1, X2 and X3.

FIGS. 3 and 4 show further examples of curve fitting.

FIG. 5 shows data correction for component drift and geometry changes.

According to one embodiment of the invention, a measuring device willtherefore consist of a source of radiation, which could be aradioisotope but is preferably an X-ray source and a detector ofbackscattered radiation located on one side of the sheet of metal to bemeasured. On the other side is a detector of radiation to measure thetransmitted beam. Computers are used to process the signal from bothdetectors and used to provide the thickness measurement. A particularembodiment of the invention is shown in FIG. 1 of the accompanyingdrawings, in which an X-ray source 1 produces a beam of radiation of anintensity I_(o). This beam, when going through the material to bemeasured 7, results in a beam of radiation of intensity I which iscaptured by a detector 5, and in a backscatter beam I_(b) which isdetected by a detector of radiation for the backscatter beam 2. In thisparticular embodiment the detector is shown as surrounding the X-raybeam. This configuration has the advantage that a larger portion of thebeam is being detected than if the detector and the source of radiationwere side by side. Depending on the type of material being measured,filters to eliminate part of the radiation beam, may be located in theappropriate beam, such as the filter 3 in the incident X-ray beam, thefilter 4 in the backscattered beam and the filter 6 in the transmittedbeam, on the backscatter detector 4, or on the transmitted beam detector5. The detectors 2 and 5 are ion chambers detectors of a type describedin "Radiation Detection and Measurement" by Glenn F. Knoll, published byJohn Wiley & Sons (Canada) in 1979. A shutter 8 consists of a metalplate capable of absorbing the beam of radiation. Differentiallyfiltered ion chambers are preferred as they have the ability to limitdetection to a certain band of energy. These are described in Rhode'sU.S. Pat. No. 3,514,602, dated May 26, 1970.

It is important that the intensity and the energy of the x-ray source bemaintained at a constant level. This is obtained by a regulatingcircuit, which may be of one of several types in existence today.

The signal processing computer accepts the signals from the ion chambers2 and 5 generally in the form of voltages proportional to the intensityof radiation received by these chambers. The computer then receives thetwo values representing the two measured quantities I and I_(b). In themost general case, the thickness X is a function of the two quantities Iand I_(b) as follows:

    X=F (I, I.sub.b)

Although analytical expressions may be found for this function, it isnot possible to use them for an actual measurement. The method forobtaining this function, which is used for a calibration operation is asfollows: A measurement is made of a large number of samples representingvarious known thicknesses within the range in which the measurement isto be made and various compositions. In representing this data in a3-dimensional space in X, I and I_(b), one finds that the pointsgenerally fall on a smooth surface. When a sheet of unknown thickness Xis placed into the beam the values of I_(b) and I are measured. Thepoint on the surface corresponding to these values is found and a valueof X determined. One needs, therefore to find a function that bestrepresents the surface in question. There are several methods that canbe used to accomplish this. One consists of using a polynomial of theform:

    X=Σa.sub.ij I.sup.i I.sub.bj

This polynomial can then be fitted to the experimental data usingseveral methods, for instance, "Curve and Surface Fitting, anIntroduction" by P. Lankaster and K. Salkauskas, published by AcademicPress in 1986.

Of course, the greater the number of coefficients in the polynomial, thegreater the accuracy. This then requires a large number of data points.

Another method which is sometime called the piecewise method consists intaking only the values of the calibration data which surround or areclose to the values obtained for the unknown sample. This is simply anextension to the three-dimensional case of what is often done in twodimensions and called curve fitting. In practice this would result asshown in FIG. 2 of the accompanying drawings in relating the measurementof the unknown sample to the three closest measurements obtained withthe samples previously measured having the thickness X1, X2 and X3. Itis then easy to obtain a plane corresponding to the equation:

    X=aI.sub.b +bI+c

and determine the coefficients a, b, c so that the plane passes throughthe three points representing the sample 123. This having been done, oneobtains essentially a function which can be then utilized for thedetermination of the unknown thickness of the sample. A variation ofthis method would be to use, not a function corresponding to a plane,but that corresponding to a quadratic function:

    X=aI.sup.2 +bII.sub.b +c I.sup.2.sub.b +d I+e I.sub.b

This requires having 6 points for calibration.

It is well known that curve or surface fitting by means of polynomialsyields good results for interpolation but not for extrapolation.Therefore, one must make absolutely certain that the unknown point isclearly circumscribed by all of the known points. On the other hand thepolynomial surface may not be fitted through a number of points, butactually pass through all of the data points. FIG. 3 of the accompanyingdrawings illustrates the two cases. A number of points are used forcalibration and the point A and B correspond to measurements made forunknown samples. To measure A, any of the methods is suitable, whereas,to measure B, the surface fit by a polynomial, using at least a squareapproximation, would be unsuitable as it is on the edge of the domain.To illustrate this point further, we show in FIG. 4 of the accompanyingdrawings, a cross section of the surface of X as a function of I andI_(b), through the line L shown in FIG. 3. This illustrates the factthat as soon as the least square approximation has left the domain whereit was constrained by the calibration data point its value can varygreatly. Thus, as an illustration we have shown the polynomial for thevalues measured by point B as yielding a wrong thickness. With some ofthe other methods, for instance, the one resulting in a planeapproximation, this would result in a cross section of the plane shownhere, of course, as a straight line, and a measurement obtained forpoint B which is closer to reality.

Other methods consists of surface fitting such as in "Tensor Products,Finite Element Methods, Moving least squares and composite methods andsurface splines" as described in the publication by P. Lancaster and K.Salkauskas mentioned above.

Additional features need to be provided to make the gauge more usable inpractice:

Corrections need to be made as indicated in FIG. 5 of the accompanyingdrawings, to compensate for drift of the various components or changesin geometry of the system. The entire operation of surface fitting bytaking a large number of samples is time consuming. It is necessary tohave another means of correcting for these in a few seconds. This can beaccomplished by inserting the same sample, i.e. standard. Preferably thethickness is roughly within the middle of the measuring range. Duringthe measurement of I_(b) and I, it may be found that these quantitieshave drifted by a certain percentage.

Instructions are given to the computer to multiply all of the values ofI_(b) and I by the percentage. This is shown automatically in FIG. 5where the raw signals are first corrected for these drifts then enteredinto the computer to obtain the first value of thickness. This value ofthickness X is then corrected again for other sources of variation. Oneof the corrections performed on X is that of temperature. If thematerial to be measured is at a different temperature, then that of thecalibrating samples and the values of X need be multiplied by a certainfactor which can be obtained experimentally, or can be easily calculatedfrom the surface expansion coefficient of the material with temperature,which is known from tables. In this case the temperature of the materialneeds to be measured by a device, not part of this invention.

Other more sophisticated means of correcting for the drift in I consistof deducting from the measured quantities the parasitic signals obtainedwith the shutter closed, denoted by the suffix sc. To correct for thedrift in I_(b), two measurements are made: one with shutter open denotedI_(bo) and with no sample in the beam. The second is made with a thicksample of a chosen alloy denoted I_(boo). It is then better to work withnormalized quantities: ##EQU1## and apply to the quantities R and B thesame methods as described above for I and I_(b) to generate thefunction:

    X=f (R, B)

We claim:
 1. A method of calculating the thickness of a sheet materialcomprising directing a beam of photons against the sheet material from aphoton source located on one side of said sheet material, detectingreflected radiation from said sheet material in a first detector locatedon the same side of said sheet material as the photon source anddetecting transmitted radiation in a second detector located on theopposite side of the said sheet material from the photon source,combining the signals of transmitted and reflected photon beams,measuring and processing the data from both detectors for a number ofcalibrating samples using a polynomial in two variables employing abest-fit method, and obtaining the thickness as a function of thedetected data and applying this function to determine the unknownthickness of a sample.
 2. A method according to claim 1, wherein thebest-fit method is a least square approximation.
 3. A method accordingto claim 1, wherein the calibration includes the step of using a sampleplaced in the beam of photons, memorizing the data representing beamintensity received by the detector and multiplying the data obtained ina measurement by the ratio of variation of the data obtained by thesample.
 4. A method according to claim 1, wherein the calibrationincludes the step of multiplying the intensities of the beam ofradiation and the reflected beam by the ratio of these values obtainedat the time of measurement to the same values obtained at the time ofcalibration.
 5. A method according to claim 1, wherein computing meansare employed to fit a linear function through three points surroundingan unknown point, said linear function being then used to calculate theunknown thickness.
 6. A method according to claim 5, wherein thecomputer functions with a quadratic function and six data points.
 7. Anapparatus for calculating the thickness of a sheet material comprising asource of photons located on one side of said sheet material, adapted todirect a beam of photons from said photon source against said sheetmaterial, a first detector located on the same side of said sheetmaterial as the photon source for detecting reflected radiation fromsaid sheet material and a second detector located on the opposite sideof the said sheet material as the photon source for detectingtransmitted radiation, the first detector concentrically surrounding thephoton beam source, computing means for combining the signals oftransmitted and reflected photon beams and computing and signalprocessing means for measuring and processing the data from bothdetectors for a number of calibrating samples using a polynomial in twovariables employing a best-fit method, and whereby the thickness of thesheet material is obtained as a function of the detected data and thefunction is applied to determine the unknown thickness of a sample. 8.Apparatus according to claim 7, wherein the source of photons is anX-ray generator.
 9. An apparatus according to claim 7, furthercomprising a regulating circuit coupled to the photon source thatmaintains the intensity and energy of the photon source at a constantlevel.
 10. A method of calculating the thickness of a sheet materialcomprising directing a beam of photons against the sheet material from aphoton source located on one side of said sheet material, detectingreflected radiation from said sheet material in a first detector locatedon the same side of said sheet material as the photon source anddetecting transmitted radiation in a second detector located on theopposite side of the said sheet material from the photon source,combining the signals of transmitted and reflected photon beams,measuring and processing the data from both detectors for a number ofcalibrating samples using a polynomial in two variables employing abest-fit method, wherein the polynomial is of the form: X=Σa_(ij) I^(i)I^(bj), and obtaining the thickness as a function of the detected dataand applying this function to determine the unknown thickness of asample.